Problem: Solve for $x$ and $y$ using substitution. ${-2x+3y = -5}$ ${y = 3x+3}$
Solution: Since $y$ has already been solved for, substitute $3x+3$ for $y$ in the first equation. ${-2x + 3}{(3x+3)}{= -5}$ Simplify and solve for $x$ $-2x+9x + 9 = -5$ $7x+9 = -5$ $7x+9{-9} = -5{-9}$ $7x = -14$ $\dfrac{7x}{{7}} = \dfrac{-14}{{7}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 3x+3}\thinspace$ to find $y$ ${y = 3}{(-2)}{ + 3}$ $y = -6 + 3$ $y = -3$ You can also plug ${x = -2}$ into $\thinspace {-2x+3y = -5}\thinspace$ and get the same answer for $y$ : ${-2}{(-2)}{ + 3y = -5}$ ${y = -3}$